Such a bundle gerbe determines, and is determined by, a
PTCP in the category of simplicial spaces. To explain this,
we first describe a simplicial space
canonically associated to a bundle gerbe \(Y_1\rightarrow Y_0^{[2]}\) ,
generalizing the Čech nerve of (REF ).
Recall, see [1]} for details, that there is a section of \(Y_1\rightarrow Y_0^{[2]}\)  defined over the diagonal \(Y_0\subset Y_0^{[2]}\) .
This map together with the two obvious maps \(Y_1\rightarrow Y_0\)  defines a 1-truncated simplicial space \(Y\) :
\({Y_1 @<2.5ex>[r]^-{d_0} [r]^-{d_1} & Y_0. @<2.5ex>[l]_-{s_0} }\) 
